201
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Ai BQ. Ratchet transport powered by chiral active particles. Sci Rep 2016; 6:18740. [PMID: 26795952 PMCID: PMC4726254 DOI: 10.1038/srep18740] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2015] [Accepted: 11/25/2015] [Indexed: 11/17/2022] Open
Abstract
We numerically investigate the ratchet transport of mixtures of active and passive particles in a transversal asymmetric channel. A big passive particle is immersed in a ‘sea’ of active particles. Due to the chirality of active particles, the longitudinal directed transport is induced by the transversal asymmetry. For the active particles, the chirality completely determines the direction of the ratchet transport, the counterclockwise and clockwise particles move to the opposite directions and can be separated. However, for the passive particle, the transport behavior becomes complicated, the direction is determined by competitions among the chirality, the self-propulsion speed, and the packing fraction. Interestingly, within certain parameters, the passive particle moves to the left, while active particles move to the right. In addition, there exist optimal parameters (the chirality, the height of the barrier, the self-propulsion speed and the packing fraction) at which the rectified efficiency takes its maximal value. Our findings could be used for the experimental pursuit of the ratchet transport powered by chiral active particles.
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Affiliation(s)
- Bao-quan Ai
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
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202
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Menzel AM, Saha A, Hoell C, Löwen H. Dynamical density functional theory for microswimmers. J Chem Phys 2016; 144:024115. [DOI: 10.1063/1.4939630] [Citation(s) in RCA: 66] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Andreas M. Menzel
- Institut für Theoretische Physik II, Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany
| | - Arnab Saha
- Institut für Theoretische Physik II, Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany
| | - Christian Hoell
- Institut für Theoretische Physik II, Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II, Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany
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203
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Schwarz-Linek J, Arlt J, Jepson A, Dawson A, Vissers T, Miroli D, Pilizota T, Martinez VA, Poon WC. Escherichia coli as a model active colloid: A practical introduction. Colloids Surf B Biointerfaces 2016; 137:2-16. [DOI: 10.1016/j.colsurfb.2015.07.048] [Citation(s) in RCA: 69] [Impact Index Per Article: 8.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2015] [Revised: 07/17/2015] [Accepted: 07/19/2015] [Indexed: 10/23/2022]
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204
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Szamel G. Theory for the dynamics of dense systems of athermal self-propelled particles. Phys Rev E 2016; 93:012603. [PMID: 26871118 DOI: 10.1103/physreve.93.012603] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2015] [Indexed: 06/05/2023]
Abstract
We present a derivation of a recently proposed theory for the time dependence of density fluctuations in stationary states of strongly interacting, athermal, self-propelled particles. The derivation consists of two steps. First, we start from the equation of motion for the joint distribution of particles' positions and self-propulsions and we integrate out the self-propulsions. In this way we derive an approximate, many-particle evolution equation for the probability distribution of the particles' positions. Second, we use this evolution equation to describe the time dependence of steady-state density correlations. We derive a memory function representation of the density correlation function and then we use a factorization approximation to obtain an approximate expression for the memory function. In the final equation of motion for the density correlation function the nonequilibrium character of the active system manifests itself through the presence of a new steady-state correlation function that quantifies spatial correlations of the velocities of the particles. This correlation function enters into the frequency term, and thus it describes the dependence of the short-time dynamics on the properties of the self-propulsions. More importantly, the correlation function of particles' velocities enters into the vertex of the memory function and through the vertex it modifies the long-time glassy dynamics.
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Affiliation(s)
- Grzegorz Szamel
- Department of Chemistry, Colorado State University, Fort Collins, Colorado 80525, USA and Laboratoire Charles Coulomb, UMR 5221 CNRS, Université Montpellier, Montpellier, France
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205
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Marini Bettolo Marconi U, Maggi C. Towards a statistical mechanical theory of active fluids. SOFT MATTER 2015; 11:8768-8781. [PMID: 26387914 DOI: 10.1039/c5sm01718a] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We present a stochastic description of a model of N mutually interacting active particles in the presence of external fields and characterize its steady state behavior in the absence of currents. To reproduce the effects of the experimentally observed persistence of the trajectories of the active particles we consider a Gaussian force having a non-vanishing correlation time τ, whose finiteness is a measure of the activity of the system. With these ingredients we show that it is possible to develop a statistical mechanical approach similar to the one employed in the study of equilibrium liquids and to obtain the explicit form of the many-particle distribution function by means of the multidimensional unified colored noise approximation. Such a distribution plays a role analogous to the Gibbs distribution in equilibrium statistical mechanics and provides complete information about the microscopic state of the system. From here we develop a method to determine the one- and two-particle distribution functions in the spirit of the Born-Green-Yvon (BGY) equations of equilibrium statistical mechanics. The resulting equations which contain extra-correlations induced by the activity allow us to determine the stationary density profiles in the presence of external fields, the pair correlations and the pressure of active fluids. In the low density regime we obtained the effective pair potential ϕ(r) acting between two isolated particles separated by a distance, r, showing the existence of an effective attraction between them induced by activity. Based on these results, in the second half of the paper we propose a mean field theory as an approach simpler than the BGY hierarchy and use it to derive a van der Waals expression of the equation of state.
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Affiliation(s)
- Umberto Marini Bettolo Marconi
- Scuola di Scienze e Tecnologie, Università di Camerino, Via Madonna delle Carceri, 62032, Camerino, INFN Perugia, Italy.
| | - Claudio Maggi
- Dipartimento di Fisica, Università di Roma Sapienza, I-00185, Rome, Italy
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206
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Hancock B, Baskaran A. Effect of reorientation statistics on torque response of self-propelled particles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:052143. [PMID: 26651682 DOI: 10.1103/physreve.92.052143] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/24/2015] [Indexed: 06/05/2023]
Abstract
We consider the dynamics of self-propelled particles subject to external torques. Two models for the reorientation of self-propulsion are considered: run-and-tumble particles and active Brownian particles. Using the standard tools of nonequilibrium statistical mechanics we show that the run and tumble particles have a more robust response to torques. This macroscopic signature of the underlying reorientation statistics can be used to differentiate between the two types of self-propelled particles.
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Affiliation(s)
- Benjamin Hancock
- Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
| | - Aparna Baskaran
- Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
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207
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Tiribocchi A, Wittkowski R, Marenduzzo D, Cates ME. Active Model H: Scalar Active Matter in a Momentum-Conserving Fluid. PHYSICAL REVIEW LETTERS 2015; 115:188302. [PMID: 26565505 DOI: 10.1103/physrevlett.115.188302] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2015] [Indexed: 05/23/2023]
Abstract
We present a continuum theory of self-propelled particles, without alignment interactions, in a momentum-conserving solvent. To address phase separation, we introduce a dimensionless scalar concentration field ϕ with advective-diffusive dynamics. Activity creates a contribution Σ_{ij}=-κ[over ^][(∂_{i}ϕ)(∂_{j}ϕ)-(∇ϕ)^{2}δ_{ij}/d] to the deviatoric stress, where κ[over ^] is odd under time reversal and d is the number of spatial dimensions; this causes an effective interfacial tension contribution that is negative for contractile swimmers. We predict that domain growth then ceases at a length scale where diffusive coarsening is balanced by active stretching of interfaces, and confirm this numerically. Thus, there is a subtle interplay of activity and hydrodynamics, even without alignment interactions.
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Affiliation(s)
- Adriano Tiribocchi
- SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
- Department of Physics and Astronomy, University of Padua, I-35131 Padova, Italy
| | - Raphael Wittkowski
- SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
- Institut für Theoretische Physik II, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - Davide Marenduzzo
- SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
| | - Michael E Cates
- SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
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208
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Paoluzzi M, Di Leonardo R, Angelani L. Self-Sustained Density Oscillations of Swimming Bacteria Confined in Microchambers. PHYSICAL REVIEW LETTERS 2015; 115:188303. [PMID: 26565506 DOI: 10.1103/physrevlett.115.188303] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2014] [Indexed: 06/05/2023]
Abstract
We numerically study the dynamics of run-and-tumble particles confined in two chambers connected by thin channels. Two dominant dynamical behaviors emerge: (i) an oscillatory pumping state, in which particles periodically fill the two vessels, and (ii) a circulating flow state, dynamically maintaining a near constant population level in the containers when connected by two channels. We demonstrate that the oscillatory behavior arises from the combination of a narrow channel, preventing bacteria reorientation, and a density-dependent motility inside the chambers.
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Affiliation(s)
- M Paoluzzi
- Dipartimento di Fisica Università Sapienza, P.le A Moro 2, 00185 Rome, Italy
| | - R Di Leonardo
- Dipartimento di Fisica Università Sapienza, P.le A Moro 2, 00185 Rome, Italy
- NANOTEC-CNR, Institute of Nanotechnology, Soft and Living Matter Laboratory, Piazzale A. Moro 2, I-00185 Roma, Italy
| | - L Angelani
- Dipartimento di Fisica Università Sapienza, P.le A Moro 2, 00185 Rome, Italy
- Istituto dei Sistemi Complessi (ISC-CNR), UOS Sapienza, P.le A Moro 2, 00185 Rome, Italy
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209
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Abstract
Small autonomous machines like biological cells or soft robots can convert energy input into control of function and form. It is desired that this behavior emerges spontaneously and can be easily switched over time. For this purpose we introduce an active matter system that is loosely inspired by biology and which we term an active colloidal cell. The active colloidal cell consists of a boundary and a fluid interior, both of which are built from identical rotating spinners whose activity creates convective flows. Similarly to biological cell motility, which is driven by cytoskeletal components spread throughout the entire volume of the cell, active colloidal cells are characterized by highly distributed energy conversion. We demonstrate that we can control the shape of the active colloidal cell and drive compartmentalization by varying the details of the boundary (hard vs. flexible) and the character of the spinners (passive vs. active). We report buckling of the boundary controlled by the pattern of boundary activity, as well as formation of core-shell and inverted Janus phase-separated configurations within the active cell interior. As the cell size is increased, the inverted Janus configuration spontaneously breaks its mirror symmetry. The result is a bubble-crescent configuration, which alternates between two degenerate states over time and exhibits collective migration of the fluid along the boundary. Our results are obtained using microscopic, non-momentum-conserving Langevin dynamics simulations and verified via a phase-field continuum model coupled to a Navier-Stokes equation.
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210
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Magiera MP, Brendel L. Trapping of interacting propelled colloidal particles in inhomogeneous media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:012304. [PMID: 26274159 DOI: 10.1103/physreve.92.012304] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2014] [Indexed: 06/04/2023]
Abstract
A trapping mechanism for propelled colloidal particles based on an inhomogeneous drive is presented and studied by means of computer simulations. In experiments this method can be realized using photophoretic Janus particles driven by a light source, which is partially blocked by a shading mask. This leads to an accumulation of particles in the passive part. An equation for an accumulation parameter is derived using the effective inhomogeneous diffusion constant generated by the inhomogeneous drive. The impact of particle interaction on the trapping mechanism is studied, as well as the interplay between passivity-induced trapping and the emergent self-clustering of systems containing a high density of active particles. The combination of both effects makes the clusters more controllable for applications.
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Affiliation(s)
- Martin P Magiera
- Faculty of Physics and CENIDE, University of Duisburg-Essen, D-47048 Duisburg, Germany
| | - Lothar Brendel
- Faculty of Physics and CENIDE, University of Duisburg-Essen, D-47048 Duisburg, Germany
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211
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Šimkus R, Meškienė R, Ledas Ž, Baronas R, Meškys R. Microtiter plate tests for segregation of bioluminescent bacteria. LUMINESCENCE 2015; 31:127-34. [PMID: 26039821 DOI: 10.1002/bio.2934] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2014] [Revised: 02/20/2015] [Accepted: 04/14/2015] [Indexed: 11/07/2022]
Abstract
It has been recently shown that bioluminescence imaging can be usefully applied to provide new insights into bacterial self-organization. In this work we employ bioluminescence imaging to record images of nutrient rich liquid cultures of the lux-gene reporter Escherichia coli in microtiter plate wells. The images show that patterns of inhomogenous bioluminescence form along the three-phase contact lines. The paper analyzes the dependencies of the average number of luminous aggregates (clouds) on various environmental factors. In particular, our results show that optimal (neutral) pH and high aeration rates determine the highest mean number of clouds, and that spatiotemporal patterns do not form in the pH buffered suspensions. In addition, a sigmoidal (switch-like) dependence of the number of aggregates on the rate of aeration was observed. The obtained bioluminescence imaging data was interpreted by employing the Keller-Segel-Fisher (KSF) model of chemotaxis and logistic growth, adapted to systems of metabolically flexible (two-state) bacteria. The modified KSF model successfully simulated the observed switch-like responses. The results of the microtiter plate tests and their simulations indicate that the segregation of bacteria with different activities proceeds in the three-phase contact line region.
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Affiliation(s)
- Remigijus Šimkus
- Vilnius University Institute of Biochemistry, Mokslininku 12, 08662, Vilnius, Lithuania
| | - Rita Meškienė
- Vilnius University Institute of Biochemistry, Mokslininku 12, 08662, Vilnius, Lithuania
| | - Žilvinas Ledas
- Vilnius University Faculty of Mathematics and Informatics, Naugarduko 24, LT-03225, Vilnius, Lithuania
| | - Romas Baronas
- Vilnius University Faculty of Mathematics and Informatics, Naugarduko 24, LT-03225, Vilnius, Lithuania
| | - Rolandas Meškys
- Vilnius University Institute of Biochemistry, Mokslininku 12, 08662, Vilnius, Lithuania
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212
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Cugliandolo LF, Gonnella G, Suma A. Rotational and translational diffusion in an interacting active dumbbell system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:062124. [PMID: 26172678 DOI: 10.1103/physreve.91.062124] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/19/2015] [Indexed: 06/04/2023]
Abstract
We study the dynamical properties of a two-dimensional ensemble of self-propelled dumbbells with only repulsive interactions. This model undergoes a phase transition between a homogeneous and a segregated phase and we focus on the former. We analyze the translational and rotational mean-square displacements in terms of the Péclet number, describing the relative role of active forces and thermal fluctuations, and of particle density. We find that the four distinct regimes of the translational mean-square displacement of the single active dumbbell survive at finite density for parameters that lead to a separation of time scales. We establish the Péclet number and density dependence of the diffusion constant in the last diffusive regime. We prove that the ratio between the diffusion constant and its value for the single dumbbell depends on temperature and active force only through the Péclet number at all densities explored. We also study the rotational mean-square displacement proving the existence of a rich behavior with intermediate regimes only appearing at finite density. The ratio of the rotational late-time diffusion constant and its vanishing density limit depends on the Péclet number and density only. At low Péclet number it is a monotonically decreasing function of density. At high Péclet number it first increases to reach a maximum and then decreases as a function of density. We interpret the latter result advocating the presence of large-scale fluctuations close to the transition, at large-enough density, that favor coherent rotation inhibiting, however, rotational motion for even larger packing fractions.
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Affiliation(s)
- Leticia F Cugliandolo
- Sorbonne Universités, Université Pierre et Marie Curie, Paris VI, Laboratoire de Physique Théorique et Hautes Énergies, 4 Place Jussieu, 75252 Paris Cedex 05, France
| | - Giuseppe Gonnella
- Dipartimento di Fisica, Università di Bari and INFN, Sezione di Bari, via Amendola 173, Bari, I-70126, Italy
| | - Antonio Suma
- SISSA-Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, 34136 Trieste Italy
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213
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Maggi C, Marconi UMB, Gnan N, Di Leonardo R. Multidimensional stationary probability distribution for interacting active particles. Sci Rep 2015; 5:10742. [PMID: 26021260 PMCID: PMC4448265 DOI: 10.1038/srep10742] [Citation(s) in RCA: 107] [Impact Index Per Article: 11.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2015] [Accepted: 04/29/2015] [Indexed: 11/13/2022] Open
Abstract
We derive the stationary probability distribution for a non-equilibrium system composed by an arbitrary number of degrees of freedom that are subject to Gaussian colored noise and a conservative potential. This is based on a multidimensional version of the Unified Colored Noise Approximation. By comparing theory with numerical simulations we demonstrate that the theoretical probability density quantitatively describes the accumulation of active particles around repulsive obstacles. In particular, for two particles with repulsive interactions, the probability of close contact decreases when one of the two particle is pinned. Moreover, in the case of isotropic confining potentials, the radial density profile shows a non trivial scaling with radius. Finally we show that the theory well approximates the “pressure” generated by the active particles allowing to derive an equation of state for a system of non-interacting colored noise-driven particles.
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Affiliation(s)
- Claudio Maggi
- Dipartimento di Fisica, Universit`a di Roma "Sapienza", Roma, I-00185, Italy
| | - Umberto Marini Bettolo Marconi
- Scuola di Scienze e Tecnologie, Universit`a di Camerino, Via Madonna delle Carceri, Camerino, INFN Perugia, 62032, Italy
| | - Nicoletta Gnan
- CNR-ISC, UOS Sapienza, P.le A. Moro2, Roma, I-00185, Italy
| | - Roberto Di Leonardo
- 1] Dipartimento di Fisica, Universit`a di Roma "Sapienza", Roma, I-00185, Italy [2] CNR-IMIP, UOS Roma, Dipartimento di Fisica Universit`a Sapienza, Roma, I-00185, Italy
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214
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ten Hagen B, Wittkowski R, Takagi D, Kümmel F, Bechinger C, Löwen H. Can the self-propulsion of anisotropic microswimmers be described by using forces and torques? JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:194110. [PMID: 25923010 DOI: 10.1088/0953-8984/27/19/194110] [Citation(s) in RCA: 39] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
The self-propulsion of artificial and biological microswimmers (or active colloidal particles) has often been modelled by using a force and a torque entering into the overdamped equations for the Brownian motion of passive particles. This seemingly contradicts the fact that a swimmer is force-free and torque-free, i.e. that the net force and torque on the particle vanish. Using different models for mechanical and diffusiophoretic self-propulsion, we demonstrate here that the equations of motion of microswimmers can be mapped onto those of passive particles with the shape-dependent grand resistance matrix and formally external effective forces and torques. This is consistent with experimental findings on the circular motion of artificial asymmetric microswimmers driven by self-diffusiophoresis. The concept of effective self-propulsion forces and torques significantly facilitates the understanding of the swimming paths, e.g. for a microswimmer under gravity. However, this concept has its limitations when the self-propulsion mechanism of a swimmer is disturbed either by another particle in its close vicinity or by interactions with obstacles, such as a wall.
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Affiliation(s)
- Borge ten Hagen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
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215
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Solon AP, Stenhammar J, Wittkowski R, Kardar M, Kafri Y, Cates ME, Tailleur J. Pressure and phase equilibria in interacting active brownian spheres. PHYSICAL REVIEW LETTERS 2015; 114:198301. [PMID: 26024201 DOI: 10.1103/physrevlett.114.198301] [Citation(s) in RCA: 192] [Impact Index Per Article: 21.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2014] [Indexed: 06/04/2023]
Abstract
We derive a microscopic expression for the mechanical pressure P in a system of spherical active Brownian particles at density ρ. Our exact result relates P, defined as the force per unit area on a bounding wall, to bulk correlation functions evaluated far away from the wall. It shows that (i) P(ρ) is a state function, independent of the particle-wall interaction; (ii) interactions contribute two terms to P, one encoding the slow-down that drives motility-induced phase separation, and the other a direct contribution well known for passive systems; and (iii) P is equal in coexisting phases. We discuss the consequences of these results for the motility-induced phase separation of active Brownian particles and show that the densities at coexistence do not satisfy a Maxwell construction on P.
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Affiliation(s)
- Alexandre P Solon
- Laboratoire, Matière et Systèmes Complexes, UMR 7057 CNRS/P7, Université Paris Diderot, 75205 Paris Cedex 13, France
| | - Joakim Stenhammar
- SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
| | - Raphael Wittkowski
- SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
| | - Mehran Kardar
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Yariv Kafri
- Department of Physics, Technion, Haifa 32000, Israel
| | - Michael E Cates
- SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
| | - Julien Tailleur
- Laboratoire, Matière et Systèmes Complexes, UMR 7057 CNRS/P7, Université Paris Diderot, 75205 Paris Cedex 13, France
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216
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Araki T, Fukai S. Controlled motion of Janus particles in periodically phase-separating binary fluids. SOFT MATTER 2015; 11:3470-3479. [PMID: 25849337 DOI: 10.1039/c4sm02357a] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We numerically investigate the propelled motions of a Janus particle in a periodically phase-separating binary fluid mixture. In this study, the surface of the particle tail prefers one of the binary fluid components and the particle head is neutral in the wettability. During the demixing period, the more wettable phase is selectively adsorbed to the particle tail. Growths of the adsorbed domains induce the hydrodynamic flow in the vicinity of the particle tail, and this asymmetric pumping flow drives the particle toward the particle head. During the mixing period, the particle motion almost ceases because the mixing primarily occurs via diffusion and the resulting hydrodynamic flow is negligibly small. Repeating this cycle unboundedly moves the Janus particle toward the head. The dependencies of the composition and the repeat frequency on the particle motion are discussed.
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Affiliation(s)
- Takeaki Araki
- Department of Physics, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan.
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217
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Elgeti J, Winkler RG, Gompper G. Physics of microswimmers--single particle motion and collective behavior: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2015; 78:056601. [PMID: 25919479 DOI: 10.1088/0034-4885/78/5/056601] [Citation(s) in RCA: 647] [Impact Index Per Article: 71.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/13/2023]
Abstract
Locomotion and transport of microorganisms in fluids is an essential aspect of life. Search for food, orientation toward light, spreading of off-spring, and the formation of colonies are only possible due to locomotion. Swimming at the microscale occurs at low Reynolds numbers, where fluid friction and viscosity dominates over inertia. Here, evolution achieved propulsion mechanisms, which overcome and even exploit drag. Prominent propulsion mechanisms are rotating helical flagella, exploited by many bacteria, and snake-like or whip-like motion of eukaryotic flagella, utilized by sperm and algae. For artificial microswimmers, alternative concepts to convert chemical energy or heat into directed motion can be employed, which are potentially more efficient. The dynamics of microswimmers comprises many facets, which are all required to achieve locomotion. In this article, we review the physics of locomotion of biological and synthetic microswimmers, and the collective behavior of their assemblies. Starting from individual microswimmers, we describe the various propulsion mechanism of biological and synthetic systems and address the hydrodynamic aspects of swimming. This comprises synchronization and the concerted beating of flagella and cilia. In addition, the swimming behavior next to surfaces is examined. Finally, collective and cooperate phenomena of various types of isotropic and anisotropic swimmers with and without hydrodynamic interactions are discussed.
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Affiliation(s)
- J Elgeti
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, D-52425 Jülich, Germany
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218
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Farage TFF, Krinninger P, Brader JM. Effective interactions in active Brownian suspensions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:042310. [PMID: 25974494 DOI: 10.1103/physreve.91.042310] [Citation(s) in RCA: 143] [Impact Index Per Article: 15.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/14/2015] [Indexed: 06/04/2023]
Abstract
Active colloids exhibit persistent motion, which can lead to motility-induced phase separation (MIPS). However, there currently exists no microscopic theory to account for this phenomenon. We report a first-principles theory, free of fit parameters, for active spherical colloids, which shows explicitly how an effective many-body interaction potential is generated by activity and how this can rationalize MIPS. For a passively repulsive system the theory predicts phase separation and pair correlations in quantitative agreement with simulation. For an attractive system the theory shows that phase separation becomes suppressed by moderate activity, consistent with recent experiments and simulations, and suggests a mechanism for reentrant cluster formation at high activity.
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Affiliation(s)
- T F F Farage
- Department of Physics, University of Fribourg, CH-1700 Fribourg, Switzerland
| | - P Krinninger
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - J M Brader
- Department of Physics, University of Fribourg, CH-1700 Fribourg, Switzerland
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219
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Kaiser A, Sokolov A, Aranson IS, Lowen H. Mechanisms of Carrier Transport Induced by a Microswimmer Bath. IEEE Trans Nanobioscience 2015; 14:260-6. [DOI: 10.1109/tnb.2014.2361652] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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220
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de Graaf J, Rempfer G, Holm C. Diffusiophoretic Self-Propulsion for Partially Catalytic Spherical Colloids. IEEE Trans Nanobioscience 2015; 14:272-88. [DOI: 10.1109/tnb.2015.2403255] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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221
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Colin R, Zhang R, Wilson LG. Fast, high-throughput measurement of collective behaviour in a bacterial population. J R Soc Interface 2015; 11:20140486. [PMID: 25030384 DOI: 10.1098/rsif.2014.0486] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
Abstract
Swimming bacteria explore their environment by performing a random walk, which is biased in response to, for example, chemical stimuli, resulting in a collective drift of bacterial populations towards 'a better life'. This phenomenon, called chemotaxis, is one of the best known forms of collective behaviour in bacteria, crucial for bacterial survival and virulence. Both single-cell and macroscopic assays have investigated bacterial behaviours. However, theories that relate the two scales have previously been difficult to test directly. We present an image analysis method, inspired by light scattering, which measures the average collective motion of thousands of bacteria simultaneously. Using this method, a time-varying collective drift as small as 50 nm s(-1) can be measured. The method, validated using simulations, was applied to chemotactic Escherichia coli bacteria in linear gradients of the attractant α-methylaspartate. This enabled us to test a coarse-grained minimal model of chemotaxis. Our results clearly map the onset of receptor methylation, and the transition from linear to logarithmic sensing in the bacterial response to an external chemoeffector. Our method is broadly applicable to problems involving the measurement of collective drift with high time resolution, such as cell migration and fluid flows measurements, and enables fast screening of tactic behaviours.
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Affiliation(s)
- R Colin
- The Rowland Institute at Harvard, 100 Edwin H. Land Boulevard, Cambridge, MA 02142, USA
| | - R Zhang
- Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
| | - L G Wilson
- The Rowland Institute at Harvard, 100 Edwin H. Land Boulevard, Cambridge, MA 02142, USA
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222
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Banigan EJ, Harris TH, Christian DA, Hunter CA, Liu AJ. Heterogeneous CD8+ T cell migration in the lymph node in the absence of inflammation revealed by quantitative migration analysis. PLoS Comput Biol 2015; 11:e1004058. [PMID: 25692801 PMCID: PMC4334969 DOI: 10.1371/journal.pcbi.1004058] [Citation(s) in RCA: 41] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2014] [Accepted: 11/22/2014] [Indexed: 11/18/2022] Open
Abstract
The three-dimensional positions of immune cells can be tracked in live tissues precisely as a function of time using two-photon microscopy. However, standard methods of analysis used in the field and experimental artifacts can bias interpretations and obscure important aspects of cell migration such as directional migration and non-Brownian walk statistics. Therefore, methods were developed for minimizing drift artifacts, identifying directional and anisotropic (asymmetric) migration, and classifying cell migration statistics. These methods were applied to describe the migration statistics of CD8+ T cells in uninflamed lymph nodes. Contrary to current models, CD8+ T cell statistics are not well described by a straightforward persistent random walk model. Instead, a model in which one population of cells moves via Brownian-like motion and another population follows variable persistent random walks with noise reproduces multiple statistical measures of CD8+ T cell migration in the lymph node in the absence of inflammation. Migration is fundamental to immune cell function, and accurate quantitative methods are crucial for analyzing and interpreting migration statistics. However, existing methods of analysis cannot uniquely describe cell behavior and suffer from various limitations. This complicates efforts to address questions such as to what extent chemotactic signals direct cellular behaviors and how random migration of many cells leads to coordinated immune response. We therefore develop methods that provide a complete description of migration with a minimum of assumptions and describe specific quantities for characterizing directional motion. Using numerical simulations and experimental data, we evaluate these measures and discuss methods to minimize the effects of experimental artifacts. These methodologies may be applied to various migrating cells or organisms. We apply our approach to an important model system, T cells migrating in lymph node. Surprisingly, we find that the canonical Brownian-walker-like model does not accurately describe migration. Instead, we find that T cells move heterogeneously and are described by a two-population model of persistent and diffusive random walkers. This model is completely different from the generalized Lévy walk model that describes activated T cells in brains infected with Toxoplasma gondii, indicating that T cells exhibit distinct migration statistics in different tissues.
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Affiliation(s)
- Edward J. Banigan
- Department of Physics and Astronomy, School of Arts and Sciences, University of Pennsylvania, Philadelphia, Philadelphia, United States of America
- Department of Physics and Astronomy, Northwestern University, Evanston, Illinois, United States of America
| | - Tajie H. Harris
- Department of Pathobiology, School of Veterinary Medicine, University of Pennsylvania, Philadelphia, Philadelphia, United States of America
- Department of Neuroscience, School of Medicine, University of Virginia, Charlottesville, Virginia, United States of America
| | - David A. Christian
- Department of Pathobiology, School of Veterinary Medicine, University of Pennsylvania, Philadelphia, Philadelphia, United States of America
| | - Christopher A. Hunter
- Department of Pathobiology, School of Veterinary Medicine, University of Pennsylvania, Philadelphia, Philadelphia, United States of America
| | - Andrea J. Liu
- Department of Physics and Astronomy, School of Arts and Sciences, University of Pennsylvania, Philadelphia, Philadelphia, United States of America
- * E-mail:
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223
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Maes C, Steffenoni S. Friction and noise for a probe in a nonequilibrium fluid. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:022128. [PMID: 25768479 DOI: 10.1103/physreve.91.022128] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/22/2014] [Indexed: 06/04/2023]
Abstract
We investigate the fluctuation dynamics of a probe around a deterministic motion induced by interactions with driven particles. The latter constitute the nonequilibrium medium in which the probe is immersed and is modeled as overdamped Langevin particle dynamics driven by nonconservative forces. The expansion that yields the friction and noise expressions for the reduced probe dynamics is based on linear response around a time-dependent nonequilibrium condition of the medium. The result contains an extension of the second fluctuation-dissipation relation between friction and noise for probe motion in a nonequilibrium fluid.
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Affiliation(s)
| | - Stefano Steffenoni
- Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig, Germany
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224
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Locatelli E, Baldovin F, Orlandini E, Pierno M. Active Brownian particles escaping a channel in single file. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:022109. [PMID: 25768460 DOI: 10.1103/physreve.91.022109] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2014] [Indexed: 06/04/2023]
Abstract
Active particles may happen to be confined in channels so narrow that they cannot overtake each other (single-file conditions). This interesting situation reveals nontrivial physical features as a consequence of the strong interparticle correlations developed in collective rearrangements. We consider a minimal two-dimensional model for active Brownian particles with the aim of studying the modifications introduced by activity with respect to the classical (passive) single-file picture. Depending on whether their motion is dominated by translational or rotational diffusion, we find that active Brownian particles in single file may arrange into clusters that are continuously merging and splitting (active clusters) or merely reproduce passive-motion paradigms, respectively. We show that activity conveys to self-propelled particles a strategic advantage for trespassing narrow channels against external biases (e.g., the gravitational field).
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Affiliation(s)
- Emanuele Locatelli
- Dipartimento di Fisica e Astronomia "G. Galilei" and Sezione CNISM, Università di Padova, Via Marzolo 8, I-35131 Padova, Italy
| | - Fulvio Baldovin
- Dipartimento di Fisica e Astronomia "G. Galilei," Sezione INFN, and Sezione CNISM, Università di Padova, Via Marzolo 8, I-35131 Padova, Italy
| | - Enzo Orlandini
- Dipartimento di Fisica e Astronomia "G. Galilei," Sezione INFN, and Sezione CNISM, Università di Padova, Via Marzolo 8, I-35131 Padova, Italy
| | - Matteo Pierno
- Dipartimento di Fisica e Astronomia "G. Galilei" and Sezione CNISM, Università di Padova, Via Marzolo 8, I-35131 Padova, Italy
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225
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Pal A. Diffusion in a potential landscape with stochastic resetting. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:012113. [PMID: 25679576 DOI: 10.1103/physreve.91.012113] [Citation(s) in RCA: 72] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/13/2014] [Indexed: 05/27/2023]
Abstract
The steady state of a Brownian particle diffusing in an arbitrary potential under the stochastic resetting mechanism has been studied. We show that there are different classes of nonequilibrium steady states depending on the nature of the potential. In the stable potential landscape, the system attains a well-defined steady state; however, the existence of the steady state for the unstable landscape is constrained. We have also investigated the transient properties of the propagator towards the steady state under the stochastic resetting mechanism. Finally, we have done numerical simulations to verify our analytical results.
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Affiliation(s)
- Arnab Pal
- Raman Research Institute, Bangalore 560080, India
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226
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Dervaux J, Magniez JC, Libchaber A. On growth and form of Bacillus subtilis biofilms. Interface Focus 2014; 4:20130051. [PMID: 25485075 DOI: 10.1098/rsfs.2013.0051] [Citation(s) in RCA: 41] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
A general feature of mature biofilms is their highly heterogeneous architecture that partitions the microbial city into sectors with specific micro-environments. To understand how this heterogeneity arises, we have investigated the formation of a microbial community of the model organism Bacillus subtilis. We first show that the growth of macroscopic colonies is inhibited by the accumulation of ammoniacal by-products. By constraining biofilms to grow approximately as two-dimensional layers, we then find that the bacteria which differentiate to produce extracellular polymeric substances form tightly packed bacterial chains. In addition to the process of cellular chaining, the biomass stickiness also strongly hinders the reorganization of cells within the biofilm. Based on these observations, we then write a biomechanical model for the growth of the biofilm where the cell density is constant and the physical mechanism responsible for the spreading of the biomass is the pressure generated by the division of the bacteria. Besides reproducing the velocity field of the biomass across the biofilm, the model predicts that, although bacteria divide everywhere in the biofilm, fluctuations in the growth rates of the bacteria lead to a coarsening of the growing bacterial layer. This process of kinetic roughening ultimately leads to the formation of a rough biofilm surface exhibiting self-similar properties. Experimental measurements of the biofilm texture confirm these predictions.
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Affiliation(s)
- Julien Dervaux
- Center for Studies in Physics and Biology , The Rockefeller University , New York, NY 10065 , USA
| | | | - Albert Libchaber
- Center for Studies in Physics and Biology , The Rockefeller University , New York, NY 10065 , USA
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227
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Maggi C, Paoluzzi M, Pellicciotta N, Lepore A, Angelani L, Di Leonardo R. Generalized energy equipartition in harmonic oscillators driven by active baths. PHYSICAL REVIEW LETTERS 2014; 113:238303. [PMID: 25526168 DOI: 10.1103/physrevlett.113.238303] [Citation(s) in RCA: 90] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2014] [Indexed: 06/04/2023]
Abstract
We study experimentally and numerically the dynamics of colloidal beads confined by a harmonic potential in a bath of swimming E. coli bacteria. The resulting dynamics is well approximated by a Langevin equation for an overdamped oscillator driven by the combination of a white thermal noise and an exponentially correlated active noise. This scenario leads to a simple generalization of the equipartition theorem resulting in the coexistence of two different effective temperatures that govern dynamics along the flat and the curved directions in the potential landscape.
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Affiliation(s)
- Claudio Maggi
- Dipartimento di Fisica, Università di Roma "Sapienza," I-00185 Roma, Italy
| | - Matteo Paoluzzi
- CNR-IPCF, UOS Roma, Dipartimento di Fisica Università Sapienza, I-00185 Roma, Italy
| | | | - Alessia Lepore
- Dipartimento di Fisica, Università di Roma "Sapienza," I-00185 Roma, Italy
| | - Luca Angelani
- CNR-IPCF, UOS Roma, Dipartimento di Fisica Università Sapienza, I-00185 Roma, Italy
| | - Roberto Di Leonardo
- Dipartimento di Fisica, Università di Roma "Sapienza," I-00185 Roma, Italy and CNR-IPCF, UOS Roma, Dipartimento di Fisica Università Sapienza, I-00185 Roma, Italy
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228
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Suma A, Gonnella G, Laghezza G, Lamura A, Mossa A, Cugliandolo LF. Dynamics of a homogeneous active dumbbell system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:052130. [PMID: 25493762 DOI: 10.1103/physreve.90.052130] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2014] [Indexed: 05/15/2023]
Abstract
We analyze the dynamics of a two-dimensional system of interacting active dumbbells. We characterize the mean-square displacement, linear response function, and deviation from the equilibrium fluctuation-dissipation theorem as a function of activity strength, packing fraction, and temperature for parameters such that the system is in its homogeneous phase. While the diffusion constant in the last diffusive regime naturally increases with activity and decreases with packing fraction, we exhibit an intriguing nonmonotonic dependence on the activity of the ratio between the finite-density and the single-particle diffusion constants. At fixed packing fraction, the time-integrated linear response function depends nonmonotonically on activity strength. The effective temperature extracted from the ratio between the integrated linear response and the mean-square displacement in the last diffusive regime is always higher than the ambient temperature, increases with increasing activity, and, for small active force, monotonically increases with density while for sufficiently high activity it first increases and next decreases with the packing fraction. We ascribe this peculiar effect to the existence of finite-size clusters for sufficiently high activity and density at the fixed (low) temperatures at which we worked. The crossover occurs at lower activity or density the lower the external temperature. The finite-density effective temperature is higher (lower) than the single dumbbell one below (above) a crossover value of the Péclet number.
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Affiliation(s)
- Antonio Suma
- SISSA-Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, 34136 Trieste, Italy
| | - Giuseppe Gonnella
- Dipartimento di Fisica, Università di Bari and INFN, Sezione di Bari, via Amendola 173, Bari I-70126, Italy
| | - Gianluca Laghezza
- Dipartimento di Fisica, Università di Bari and INFN, Sezione di Bari, via Amendola 173, Bari I-70126, Italy
| | - Antonio Lamura
- Istituto Applicazioni Calcolo, CNR, via Amendola 122/D, Bari I-70126, Italy
| | - Alessandro Mossa
- Dipartimento di Fisica, Università di Bari and INFN, Sezione di Bari, via Amendola 173, Bari I-70126, Italy
| | - Leticia F Cugliandolo
- Sorbonne Universités, Université Pierre et Marie Curie, Paris 6, Laboratoire de Physique Théorique et Hautes Energies, 4, Place Jussieu, Tour 13, 5ème étage, 75252 Paris Cedex 05, France
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229
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Reichhardt C, Olson Reichhardt CJ. Absorbing phase transitions and dynamic freezing in running active matter systems. SOFT MATTER 2014; 10:7502-7510. [PMID: 25123498 DOI: 10.1039/c4sm01273a] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We examine a two-dimensional system of sterically repulsive interacting disks where each particle runs in a random direction. This system is equivalent to a run-and-tumble dynamics system in the limit where the run time is infinite. At low densities, we find a strongly fluctuating state composed of transient clusters. Above a critical density that is well below the density at which non-active particles would crystallize, the system can organize into a drifting quiescent or frozen state where the fluctuations are lost and large crystallites form surrounded by a small density of individual particles. Although all the particles are still moving, their paths form closed orbits. The average transient time to organize into the quiescent state diverges as a power law upon approaching the critical density from above. We compare our results to the random organization observed for periodically sheared systems that can undergo an absorbing transition from a fluctuating state to a dynamical non-fluctuating state. In the random organization studies, the system organizes to a state in which the particles no longer interact; in contrast, we find that the randomly running active matter organizes to a strongly interacting dynamically jammed state. We show that the transition to the frozen state is robust against a certain range of stochastic fluctuations. We also examine the effects of adding a small number of pinned particles to the system and find that the transition to the frozen state shifts to significantly lower densities and arises via the nucleation of faceted crystals centered at the obstacles.
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Affiliation(s)
- Charles Reichhardt
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
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230
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Paoluzzi M, Di Leonardo R, Angelani L. Run-and-tumble particles in speckle fields. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2014; 26:375101. [PMID: 25105250 DOI: 10.1088/0953-8984/26/37/375101] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
The random energy landscapes developed by speckle fields can be used to confine and manipulate a large number of micro-particles with a single laser beam. By means of molecular dynamics simulations, we investigate the static and dynamic properties of an active suspension of swimming bacteria embedded into speckle patterns. Looking at the correlation of the density fluctuations and the equilibrium density profiles, we observe a crossover phenomenon when the forces exerted by the speckles are equal to the bacteria's propulsion.
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Affiliation(s)
- M Paoluzzi
- CNR-IPCF, UOS Roma, Dipartimento di Fisica, Università Sapienza, P.le Aldo Moro 2, I-00185, Rome, Italy
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231
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Yang X, Manning ML, Marchetti MC. Aggregation and segregation of confined active particles. SOFT MATTER 2014; 10:6477-6484. [PMID: 25046587 DOI: 10.1039/c4sm00927d] [Citation(s) in RCA: 149] [Impact Index Per Article: 14.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We simulate a model of self-propelled disks with soft repulsive interactions confined to a box in two dimensions. For small rotational diffusion rates, monodisperse disks spontaneously accumulate at the walls. At low densities, interaction forces between particles are strongly inhomogeneous, and a simple model predicts how these inhomogeneities alter the equation of state. At higher densities, collective effects become important. We observe signatures of a jamming transition at a packing fraction ϕ ∼ 0.88, which is also the jamming point for non-active athermal monodisperse disks. At this ϕ, the system develops a critical finite active speed necessary for wall aggregation. At packing fractions above ϕ ∼ 0.6, the pressure decreases with increasing density, suggesting that strong interactions between particles are affecting the equation of state well below the jamming transition. A mixture of bidisperse disks segregates in the absence of any adhesion, identifying a new mechanism that could contribute to cell sorting in embryonic development.
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Affiliation(s)
- Xingbo Yang
- Physics Department, Syracuse University, Syracuse, NY 13244, USA.
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232
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Kumar N, Soni H, Ramaswamy S, Sood AK. Flocking at a distance in active granular matter. Nat Commun 2014; 5:4688. [PMID: 25181961 DOI: 10.1038/ncomms5688] [Citation(s) in RCA: 135] [Impact Index Per Article: 13.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2014] [Accepted: 07/14/2014] [Indexed: 11/09/2022] Open
Abstract
The self-organized motion of vast numbers of creatures in a single direction is a spectacular example of emergent order. Here, we recreate this phenomenon using actuated nonliving components. We report here that millimetre-sized tapered rods, rendered motile by contact with an underlying vibrated surface and interacting through a medium of spherical beads, undergo a phase transition to a state of spontaneous alignment of velocities and orientations above a threshold bead area fraction. Guided by a detailed simulation model, we construct an analytical theory of this flocking transition, with two ingredients: a moving rod drags beads; neighbouring rods reorient in the resulting flow like a weathercock in the wind. Theory and experiment agree on the structure of our phase diagram in the plane of rod and bead concentrations and power-law spatial correlations near the phase boundary. Our discovery suggests possible new mechanisms for the collective transport of particulate or cellular matter.
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Affiliation(s)
- Nitin Kumar
- Department of Physics, Indian Institute of Science, Bangalore 560 012, India
| | - Harsh Soni
- 1] Department of Physics, Indian Institute of Science, Bangalore 560 012, India [2] TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, 21 Brundavan Colony, Osman Sagar Road, Narsingi, Hyderabad 500 075, India
| | - Sriram Ramaswamy
- 1] Department of Physics, Indian Institute of Science, Bangalore 560 012, India [2] TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, 21 Brundavan Colony, Osman Sagar Road, Narsingi, Hyderabad 500 075, India
| | - A K Sood
- Department of Physics, Indian Institute of Science, Bangalore 560 012, India
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233
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Matas-Navarro R, Golestanian R, Liverpool TB, Fielding SM. Hydrodynamic suppression of phase separation in active suspensions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:032304. [PMID: 25314443 DOI: 10.1103/physreve.90.032304] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/19/2012] [Indexed: 05/15/2023]
Abstract
We simulate with hydrodynamics a suspension of active disks squirming through a Newtonian fluid. We explore numerically the full range of squirmer area fractions from dilute to close packed and show that "motility induced phase separation," which was recently proposed to arise generically in active matter, and which has been seen in simulations of active Brownian disks, is strongly suppressed by hydrodynamic interactions. We give an argument for why this should be the case and support it with counterpart simulations of active Brownian disks in a parameter regime that provides a closer counterpart to hydrodynamic suspensions than in previous studies.
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Affiliation(s)
- Ricard Matas-Navarro
- Department of Physics, University of Durham, Science Laboratories, South Road, Durham, DH1 3LE, UK
| | - Ramin Golestanian
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford, OX1 3NP, UK
| | | | - Suzanne M Fielding
- Department of Physics, University of Durham, Science Laboratories, South Road, Durham, DH1 3LE, UK
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234
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Tarama M, Menzel AM, Löwen H. Deformable microswimmer in a swirl: capturing and scattering dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:032907. [PMID: 25314504 DOI: 10.1103/physreve.90.032907] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/15/2014] [Indexed: 06/04/2023]
Abstract
Inspired by the classical Kepler and Rutherford problem, we investigate an analogous setup in the context of active microswimmers: the behavior of a deformable microswimmer in a swirl flow. First, we identify new steady bound states in the swirl flow and analyze their stability. Second, we study the dynamics of a self-propelled swimmer heading towards the vortex center, and we observe the subsequent capturing and scattering dynamics. We distinguish between two major types of swimmers, those that tend to elongate perpendicularly to the propulsion direction and those that pursue a parallel elongation. While the first ones can get caught by the swirl, the second ones were always observed to be scattered, which proposes a promising escape strategy. This offers a route to design artificial microswimmers that show the desired behavior in complicated flow fields. It should be straightforward to verify our results in a corresponding quasi-two-dimensional experiment using self-propelled droplets on water surfaces.
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Affiliation(s)
- Mitsusuke Tarama
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan and Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany and Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan
| | - Andreas M Menzel
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
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235
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Koumakis N, Maggi C, Di Leonardo R. Directed transport of active particles over asymmetric energy barriers. SOFT MATTER 2014; 10:5695-5701. [PMID: 24978345 DOI: 10.1039/c4sm00665h] [Citation(s) in RCA: 52] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We theoretically and numerically investigate the transport of active colloids to target regions, delimited by asymmetric energy barriers. We show that it is possible to introduce a generalized effective temperature that is related to the local variance of particle velocities. The stationary probability distributions can be derived from a simple diffusion equation in the presence of an inhomogeneous effective temperature resulting from the action of external force fields. In particular, transition rates over asymmetric energy barriers can be unbalanced by having different effective temperatures over the two slopes of the barrier. By varying the type of active noise, we find that equal values of diffusivity and persistence time may produce strongly varied effective temperatures and thus stationary distributions.
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Affiliation(s)
- N Koumakis
- National Research Council of Italy-IPCF UOS Roma, 00185, Rome, Italy.
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236
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Fily Y, Baskaran A, Hagan MF. Dynamics of self-propelled particles under strong confinement. SOFT MATTER 2014; 10:5609-17. [PMID: 24965311 DOI: 10.1039/c4sm00975d] [Citation(s) in RCA: 137] [Impact Index Per Article: 13.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
We develop a statistical theory for the dynamics of non-aligning, non-interacting self-propelled particles confined in a convex box in two dimensions. We find that when the size of the box is small compared to the persistence length of a particle's trajectory (strong confinement), the steady-state density is zero in the bulk and proportional to the local curvature on the boundary. Conversely, the theory may be used to construct the box shape that yields any desired density distribution on the boundary, thus offering a general tool to understand and design such confinements. When the curvature variations are small, we also predict the distribution of orientations at the boundary and the exponential decay of pressure as a function of box size recently observed in simulations in a spherical box.
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Affiliation(s)
- Yaouen Fily
- Martin A. Fisher School of Physics, Brandeis University, Waltham, MA 02454, USA.
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237
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Furukawa A, Marenduzzo D, Cates ME. Activity-induced clustering in model dumbbell swimmers: the role of hydrodynamic interactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:022303. [PMID: 25215734 DOI: 10.1103/physreve.90.022303] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2014] [Indexed: 06/03/2023]
Abstract
Using a fluid-particle dynamics approach, we numerically study the effects of hydrodynamic interactions on the collective dynamics of active suspensions within a simple model for bacterial motility: each microorganism is modeled as a stroke-averaged dumbbell swimmer with prescribed dipolar force pairs. Using both simulations and qualitative arguments, we show that, when the separation between swimmers is comparable to their size, the swimmers' motions are strongly affected by activity-induced hydrodynamic forces. To further understand these effects, we investigate semidilute suspensions of swimmers in the presence of thermal fluctuations. A direct comparison between simulations with and without hydrodynamic interactions shows these to enhance the dynamic clustering at a relatively small volume fraction; with our chosen model the key ingredient for this clustering behavior is hydrodynamic trapping of one swimmer by another, induced by the active forces. Furthermore, the density dependence of the motility (of both the translational and rotational motions) exhibits distinctly different behaviors with and without hydrodynamic interactions; we argue that this is linked to the clustering tendency. Our study illustrates the fact that hydrodynamic interactions not only affect kinetic pathways in active suspensions, but also cause major changes in their steady state properties.
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Affiliation(s)
- Akira Furukawa
- Institute of Industrial Science, University of Tokyo, Meguro-ku, Tokyo 153-8505, Japan
| | - Davide Marenduzzo
- School of Physics and Astronomy, University of Edinburgh, JCMB Kings Buildings, Mayfield Road, Edinburgh EH9 3JZ, United Kingdom
| | - Michael E Cates
- School of Physics and Astronomy, University of Edinburgh, JCMB Kings Buildings, Mayfield Road, Edinburgh EH9 3JZ, United Kingdom
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238
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Wittkowski R, Tiribocchi A, Stenhammar J, Allen RJ, Marenduzzo D, Cates ME. Scalar φ4 field theory for active-particle phase separation. Nat Commun 2014; 5:4351. [DOI: 10.1038/ncomms5351] [Citation(s) in RCA: 198] [Impact Index Per Article: 19.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2013] [Accepted: 06/09/2014] [Indexed: 11/09/2022] Open
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239
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Potiguar FQ, Farias GA, Ferreira WP. Self-propelled particle transport in regular arrays of rigid asymmetric obstacles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:012307. [PMID: 25122303 DOI: 10.1103/physreve.90.012307] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/24/2013] [Indexed: 06/03/2023]
Abstract
We report numerical results which show the achievement of net transport of self-propelled particles (SPPs) in the presence of a two-dimensional regular array of convex, either symmetric or asymmetric, rigid obstacles. The repulsive interparticle (soft disks) and particle-obstacle interactions present no alignment rule. We find that SPPs present a vortex-type motion around convex symmetric obstacles even in the absence of hydrodynamic effects. Such a motion is not observed for a single SPP, but is a consequence of the collective motion of SPPs around the obstacles. A steady particle current is spontaneously established in an array of nonsymmetric convex obstacles (which presents no cavity in which particles may be trapped), and in the absence of an external field. Our results are mainly a consequence of the tendency of the self-propelled particles to attach to solid surfaces.
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Affiliation(s)
- Fabricio Q Potiguar
- Universidade Federal do Pará, Faculdade de Física, ICEN, Avenida Augusto Correa 1, Guamá, 66075-110 Belém, Pará, Brazil
| | - G A Farias
- Departamento de Física, Universidade Federal do Ceará, Caixa Postal 6030, Campus do Pici, 60455-760 Fortaleza, Ceará, Brazil
| | - W P Ferreira
- Departamento de Física, Universidade Federal do Ceará, Caixa Postal 6030, Campus do Pici, 60455-760 Fortaleza, Ceará, Brazil
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240
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Angelani L, Di Leonardo R, Paoluzzi M. First-passage time of run-and-tumble particles. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2014; 37:15. [PMID: 25015558 DOI: 10.1140/epje/i2014-14059-4] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/09/2014] [Revised: 06/06/2014] [Accepted: 06/13/2014] [Indexed: 06/03/2023]
Abstract
We solve the problem of first-passage time for run-and-tumble particles in one dimension. Exact expression is derived for the mean first-passage time in the general case, considering external force fields and chemotactic fields, giving rise to space-dependent swim speed and tumble rate. Agreement between theoretical formulae and numerical simulations is obtained in the analyzed case studies --constant and sinusoidal force fields, constant gradient chemotactic field. Reported findings can be useful to get insights into very different phenomena involving active particles, such as bacterial motion in external fields, intracellular transport, cell migration, animal foraging.
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Affiliation(s)
- L Angelani
- CNR-IPCF, UOS Roma c/o Dip. di Fisica Università "Sapienza", I-00185, Roma, Italy,
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241
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Ray D, Reichhardt C, Reichhardt CJO. Casimir effect in active matter systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:013019. [PMID: 25122381 DOI: 10.1103/physreve.90.013019] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2014] [Indexed: 06/03/2023]
Abstract
We numerically examine run-and-tumble active matter particles in Casimir geometries composed of two finite parallel walls. We find that there is an attractive force between the two walls of a magnitude that increases with increasing run length. The attraction exhibits an unusual exponential dependence on the wall separation, and it arises due to a depletion of swimmers in the region between the walls by a combination of the motion of the particles along the walls and a geometric shadowing effect. This attraction is robust as long as the wall length is comparable to or smaller than the swimmer run length, and is only slightly reduced by the inclusion of steric interactions between swimmers. We also examine other geometries and find regimes in which there is a crossover from attraction to repulsion between the walls as a function of wall separation and wall length.
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Affiliation(s)
- D Ray
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA and Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556, USA
| | - C Reichhardt
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - C J Olson Reichhardt
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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242
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Szamel G. Self-propelled particle in an external potential: existence of an effective temperature. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:012111. [PMID: 25122255 DOI: 10.1103/physreve.90.012111] [Citation(s) in RCA: 138] [Impact Index Per Article: 13.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2014] [Indexed: 06/03/2023]
Abstract
We study a stationary state of a single self-propelled, athermal particle in linear and quadratic external potentials. The self-propulsion is modeled as a fluctuating internal driving force evolving according to the Ornstein-Uhlenbeck process, independently of the state of the particle. Without an external potential, in the long time limit, the self-propelled particle moving in a viscous medium performs diffusive motion, which allows one to identify an effective temperature. We show that in the presence of a linear external potential the stationary state distribution has an exponential form with the sedimentation length determined by the effective temperature of the free self-propelled particle. In the presence of a quadratic external potential the stationary state distribution has a Gaussian form. However, in general, this distribution is not determined by the effective temperature of the free self-propelled particle.
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Affiliation(s)
- Grzegorz Szamel
- Department of Chemistry, Colorado State University, Fort Collins, Colorado 80525, USA
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243
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Reichhardt C, Olson Reichhardt CJ. Active matter transport and jamming on disordered landscapes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:012701. [PMID: 25122329 DOI: 10.1103/physreve.90.012701] [Citation(s) in RCA: 70] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2014] [Indexed: 06/03/2023]
Abstract
We numerically examine the transport of active run-and-tumble particles with steric particle-particle interactions driven with a drift force over random disordered landscapes composed of fixed obstacles. For increasing run lengths, the net particle transport initially increases before reaching a maximum and decreasing at larger run lengths. The transport reduction is associated with the formation of cluster or living crystal states that become locally jammed or clogged by the obstacles. We also find that the system dynamically jams at lower particle densities when the run length is increased. Our results indicate that there is an optimal activity level for transport of run-and-tumble type active matter through quenched disorder and could be important for understanding biological transport in complex environments or for applications of active matter particles in random media.
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Affiliation(s)
- C Reichhardt
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - C J Olson Reichhardt
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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244
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Hennes M, Wolff K, Stark H. Self-induced polar order of active Brownian particles in a harmonic trap. PHYSICAL REVIEW LETTERS 2014; 112:238104. [PMID: 24972231 DOI: 10.1103/physrevlett.112.238104] [Citation(s) in RCA: 45] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/06/2014] [Indexed: 06/03/2023]
Abstract
Hydrodynamically interacting active particles in an external harmonic potential form a self-assembled fluid pump at large enough Péclet numbers. Here, we give a quantitative criterion for the formation of the pump and show that particle orientations align in the self-induced flow field in surprising analogy to ferromagnetic order where the active Péclet number plays the role of inverse temperature. The particle orientations follow a Boltzmann distribution Φ(p) ∼ exp(Ap(z)) where the ordering mean field A scales with the active Péclet number and polar order parameter. The mean flow field in which the particles' swimming directions align corresponds to a regularized Stokeslet with strength proportional to swimming speed. Analytic mean-field results are compared with results from Brownian dynamics simulations with hydrodynamic interactions included and are found to capture the self-induced alignment very well.
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Affiliation(s)
- Marc Hennes
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
| | - Katrin Wolff
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
| | - Holger Stark
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
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245
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Berthier L. Nonequilibrium glassy dynamics of self-propelled hard disks. PHYSICAL REVIEW LETTERS 2014; 112:220602. [PMID: 24949749 DOI: 10.1103/physrevlett.112.220602] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2013] [Indexed: 06/03/2023]
Abstract
We analyze the collective dynamics of self-propelled particles in the large-density regime where passive particles undergo a kinetic arrest to an amorphous glassy state. We capture the competition between self-propulsion and crowding effects using a two-dimensional model of self-propelled hard disks, which we study using Monte Carlo simulations. Although the activity drives the system far from equilibrium, self-propelled particles undergo a kinetic arrest, which we characterize in detail and compare with its equilibrium counterpart. In particular, the critical density for dynamic arrest continuously shifts to larger densities with increasing activity, and the relaxation time is surprisingly well described by an algebraic divergence resulting from the emergence of highly collective dynamics. These results show that dense assemblies of active particles undergo a nonequilibrium glass transition that is profoundly affected by self-propulsion mechanisms.
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Affiliation(s)
- Ludovic Berthier
- Laboratoire Charles Coulomb, UMR 5221, CNRS and Université Montpellier 2, Montpellier, France
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246
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Levis D, Berthier L. Clustering and heterogeneous dynamics in a kinetic Monte Carlo model of self-propelled hard disks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:062301. [PMID: 25019770 DOI: 10.1103/physreve.89.062301] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2014] [Indexed: 06/03/2023]
Abstract
We introduce a kinetic Monte Carlo model for self-propelled hard disks to capture with minimal ingredients the interplay between thermal fluctuations, excluded volume, and self-propulsion in large assemblies of active particles. We analyze in detail the resulting (density, self-propulsion) nonequilibrium phase diagram over a broad range of parameters. We find that purely repulsive hard disks spontaneously aggregate into fractal clusters as self-propulsion is increased and rationalize the evolution of the average cluster size by developing a kinetic model of reversible aggregation. As density is increased, the nonequilibrium clusters percolate to form a ramified structure reminiscent of a physical gel. We show that the addition of a finite amount of noise is needed to trigger a nonequilibrium phase separation, showing that demixing in active Brownian particles results from a delicate balance between noise, interparticle interactions, and self-propulsion. We show that self-propulsion has a profound influence on the dynamics of the active fluid. We find that the diffusion constant has a nonmonotonic behavior as self-propulsion is increased at finite density and that activity produces strong deviations from Fickian diffusion that persist over large time scales and length scales, suggesting that systems of active particles generically behave as dynamically heterogeneous systems.
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Affiliation(s)
- Demian Levis
- Laboratoire Charles Coulomb, UMR 5221 CNRS, and Université Montpellier 2, Montpellier, France
| | - Ludovic Berthier
- Laboratoire Charles Coulomb, UMR 5221 CNRS, and Université Montpellier 2, Montpellier, France
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247
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Camley BA, Rappel WJ. Velocity alignment leads to high persistence in confined cells. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:062705. [PMID: 25019812 PMCID: PMC4458368 DOI: 10.1103/physreve.89.062705] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2014] [Indexed: 05/23/2023]
Abstract
Many cell types display random motility on two-dimensional substrates but crawl persistently in a single direction when confined in a microchannel or on an adhesive micropattern. Does this imply that the motility mechanism of confined cells is fundamentally different from that of unconfined cells? We argue that both free- and confined-cell migration may be described by a generic model of cells as "velocity-aligning" active Brownian particles previously proposed to solve a completely separate problem in collective cell migration. Our model can be mapped to a diffusive escape over a barrier and analytically solved to determine the cell's orientation distribution and repolarization rate. In quasi-one-dimensional confinement, velocity-aligning cells maintain their direction for times that can be exponentially larger than their persistence time in the absence of confinement. Our results suggest an important connection between single- and collective-cell migration: high persistence in confined cells corresponds with fast alignment of velocity to cell-cell forces.
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Affiliation(s)
- Brian A Camley
- Department of Physics and Center for Theoretical Biological Physics, University of California, San Diego, La Jolla, California 92093, USA
| | - Wouter-Jan Rappel
- Department of Physics and Center for Theoretical Biological Physics, University of California, San Diego, La Jolla, California 92093, USA
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248
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Piazza R. Settled and unsettled issues in particle settling. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2014; 77:056602. [PMID: 24801715 DOI: 10.1088/0034-4885/77/5/056602] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/15/2023]
Abstract
Colloid sedimentation has played a seminal role in the development of statistical physics thanks to the celebrated experiments by Perrin, which provided a concrete demonstration of molecular reality and gave strong support to Einstein's theory of Brownian motion. This review, which mostly focuses on settling at low Peclét number, where Brownian fluctuations are dominant, aims to show that a lot more can be learnt both from the sedimentation equilibrium and from the particle settling dynamics of a wide class of systems, ranging from simple colloids to mesogenic suspensions, from soft solids to active particles and living organisms. At the same time, the occurrence of unexpected and surprising effects brings about challenging questions in statistical and fluid mechanics that make sedimentation an exciting field of research.
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Affiliation(s)
- Roberto Piazza
- Department of Chemistry, Material Science, and Chemical Engineering Politecnico di Milano, via Ponzio 34/3, 20133 Milano, Italy
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249
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Koumakis N, Lepore A, Maggi C, Di Leonardo R. Targeted delivery of colloids by swimming bacteria. Nat Commun 2014; 4:2588. [PMID: 24100868 PMCID: PMC4112550 DOI: 10.1038/ncomms3588] [Citation(s) in RCA: 99] [Impact Index Per Article: 9.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2013] [Accepted: 09/10/2013] [Indexed: 11/22/2022] Open
Abstract
The possibility of exploiting motile microorganisms as tiny propellers represents a fascinating strategy for the transport of colloidal cargoes. However, delivery on target sites usually requires external control fields to steer propellers and trigger cargo release. The need for a constant feedback mechanism prevents the design of compact devices where biopropellers could perform their tasks autonomously. Here we show that properly designed three-dimensional (3D) microstructures can define accumulation areas where bacteria spontaneously and efficiently store colloidal beads. The process is stochastic in nature and results from the rectifying action of an asymmetric energy landscape over the fluctuating forces arising from collisions with swimming bacteria. As a result, the concentration of colloids over target areas can be strongly increased or depleted according to the topography of the underlying structures. Besides the significance to technological applications, our experiments pose some important questions regarding the structure of stationary probability distributions in non-equilibrium systems. Transport of colloidal cargoes to target sites can be done by controlling active carriers, like self-propelled bacteria, under external stimuli. Koumakis et al. show that bacteria can autonomously achieve the same goal when moving over pre-designed asymmetric microstructures.
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Affiliation(s)
- N Koumakis
- CNR-IPCF UOS Roma c/o Dipartimento Fisica, Università di Roma 'Sapienza', 00185 Rome, Italy
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250
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Morozov A, Marenduzzo D. Enhanced diffusion of tracer particles in dilute bacterial suspensions. SOFT MATTER 2014; 10:2748-2758. [PMID: 24668266 DOI: 10.1039/c3sm52201f] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Swimming bacteria create long-range velocity fields that stir a large volume of fluid and move around passive particles dispersed in the fluid. Recent experiments and simulations have shown that long-time mean-squared displacement of passive particles in a bath of swimming bacteria exhibits diffusive behaviour with an effective diffusion coefficient significantly larger than its thermal counterpart. A comprehensive theoretical prediction of this effective diffusion coefficient and the understanding of the enhancement mechanism remain a challenge. Here, we adapt the kinetic theory by Lin et al., J. Fluid Mech., 2011, 669, 167 developed for 'squirmers' to the bacterial case to quantitatively predict enhanced diffusivity of tracer particles in dilute two- and three-dimensional suspensions of swimming bacteria. We demonstrate that the effective diffusion coefficient is a product of the bacterial number density, their swimming speed, a geometric factor characterising the velocity field created by a single bacterium, and a numerical factor. We show that the numerical factor is, in fact, a rather strong function of the system parameters, most notably the run length of the bacteria, and that these dependencies have to be taken into account to quantitatively predict the enhanced diffusivity. We perform molecular-dynamics-type simulations to confirm the conclusions of the kinetic theory. Our results are in good agreement with the values of enhanced diffusivity measured in recent two- and three-dimensional experiments.
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Affiliation(s)
- Alexander Morozov
- SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh, UK.
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